the australian curriculum v3

7/27/2019 The Australian Curriculum v3

1/18

Number and Algebra

Number and place value

Establish understanding of the language and

processes of counting by naming numbers in

sequences, initially to and from 20, moving from anystarting point (ACMNA001)

Connect number names, numerals and quantities,

including zero, initially up to 10 and then beyond

(ACMNA002)

Subitise small collections of objects (ACMNA003)

Compare, order and make correspondences between

collections, initially to 20, and explain reasoning

(ACMNA289)

Represent practical situations to model addition and

sharing (ACMNA004)

Patterns and algebra

Sort and classify familiar objects and explain the basis

for these classifications. Copy, continue and create

patterns with objects and drawings (ACMNA005)

Measurement and Geometry

Using units of measurement

Use direct and indirect comparisons to decide which

is longer, heavier or holds more, and explain

reasoning in everyday language (ACMMG006)

Compare and order the duration of events using the

everyday language of time (ACMMG007)

Connect days of the week to familiar events and

actions (ACMMG008)

Shape

Sort, describe and name familiar two-dimensional

shapes and three-dimensional objects in the

environment (ACMMG009)

Location and transformation

Describe position and movement (ACMMG010)

Statistic

Data re

Answer

(ACMSP

Mathematics

F 1 2 3 4 5 6 7 8 9 10 10A

Foundation Year

Foundation Year Level Descr iption

The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content

across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probability. The

proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored or

developed. They provide the language to build in the developmental aspects of the learning of mathematics.

At this year level:

Understanding includes connecting names, numerals and quantities

Fluency includes readily counting numbers in sequences, continuing patterns, and comparing the lengths of objects

Problem Solving includes using materials to model authentic problems, sorting objects, using familiar counting sequences to

solve unfamiliar problems, and discussing the reasonableness of the answer

Reasoning includes explaining comparisons of quantities, creating patterns, and explaining processes for indirect comparison of

length

Foundation Year Content Descriptions

Foundation Year Achievement Standard

By the end of the Foundation year, students make connections between number names, numerals and quantities up to 10. They

compare objects using mass, length and capacity. Students connect events and the days of the week. They explain the order

and duration of events. They use appropriate language to describe location.

Students count to and from 20 and order small collections. They group objects based on common characteristics and sort

shapes and objects. Students answer simple questions to collect information.

Australian Curriculum v3.0 Mathematics Foundation to Year 10 Cur... http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10

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2/18

Number and Algebra


Develop confidence with number sequences to and

from 100 by ones from any starting point. Skip count

by twos, fives and tens starting from zero

(ACMNA012)

Recognise, model, read, write and order numbers to

at least 100. Locate these numbers on a number line

(ACMNA013)

Count collections to 100 by partitioning numbers using

place value (ACMNA014)

Represent and solve simple addition and subtraction

problems using a range of strategies including

counting on, partitioning and rearranging parts

(ACMNA015)

Fractions and decimals

Recognise and describe one-half as one of two equal

parts of a whole. (ACMNA016)

Money and financial mathematics

Recognise, describe and order Australian coins

according to their value (ACMNA017)


Investigate and describe number patterns formed by

skip counting and patterns with objects (ACMNA018)



Measure and compare the lengths and capacities of

pairs of objects using uniform informal units

(ACMMG019)

Tell time to the half-hour (ACMMG020)

Describe duration using months, weeks, days and

hours (ACMMG021)

Shape

Recognise and classify familiar two-dimensional

shapes and three-dimensional objects using obvious

features (ACMMG022)


Give and follow directions to familiar locations

(ACMMG023)

Statistic

Chance

Identify

and des

will hap

(ACMSP

Data re

Choose

(ACMSP

Repres

object o

the displ

Foundation Year Work Samples

Foundation Year Mathematics Portfolio

Year 1

Year 1 Level DescriptionThe proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral part of mathematics content




At this year level: Understanding includes connecting names, numerals and quantities, and partitioning numbers in various ways

Fluency includes counting number in sequences readily forward and backwards, locating numbers on a line, and naming the

days of the week

Problem Solving includes using materials to model authentic problems, giving and receiving directions to unfamiliar places, and

using familiar counting sequences to solve unfamiliar problems and discusing the reasonableness of the answer

Reasoning includes explaining direct and indirect comparisons of length using uniform informal units, justifying representations of

data, and explaining patterns that have been created

Year 1 Content Descriptions

Year 1 Achievement Standard


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3/18

Number and Algebra


Investigate number sequences, initially those

increasing and decreasing by twos, threes, fives and

ten from any starting point, then moving to other

sequences. (ACMNA026)

Recognise, model, represent and order numbers to at

least 1000 (ACMNA027)

Group, partition and rearrange collections up to 1000

in hundreds, tens and ones to facilitate more efficient

counting (ACMNA028)

Explore the connection between addition and

subtraction (ACMNA029)

Solve simple addition and subtraction problems using

a range of efficient mental and written strategies

(ACMNA030)



Compare and order several shapes and objects

based on length, area, volume and capacity using

appropriate uniform informal units (ACMMG037)

Compare masses of objects using balance scales

(ACMMG038)

Tell time to the quarter-hour, using the language of

'past' and 'to' (ACMMG039)

Name and order months and seasons (ACMMG040)

Use a calendar to identify the date and determine the

number of days in each month (ACMMG041)

Shape

Describe and draw two-dimensional shapes, with and

without digital technologies (ACMMG042)

Statistic

Chance

Identify

involve

unlikely

impossi

Data re

Identify

categori

questio

Collect,

Create

graphs

By the end of Year 1, students describe number sequences resulting from skip counting by 2s, 5s and 10s. They identify

representations of one half. They recognise Australian coins according to their value. Students explain time durations. They

describe two-dimensional shapes and three-dimensional objects. Students describe data displays.

Students count to and from 100 and locate numbers on a number line. They carry out simple additions and subtractions using

counting strategies. They partition numbers using place value. They continue simple patterns involving numbers and objects.

Students order objects based on lengths and capacities using informal units. They tell time to the half hour. They use the

language of direction to move from place to place. Students classify outcomes of simple familiar events. They collect data by

asking questions and draw simple data displays.

Year 1 Work Samples

Year 1 Mathematics Portfolio

Year 2

Year 2 Level Description


across the three content strands: Number and Algebra, Measurement and Geometry, and Statistics and Probabil ity. The

proficiencies reinforce the significance of working mathematically within the content and describe how the content is explored ordeveloped. They provide the language to build in the developmental aspects of the learning of mathematics.

At this year level:

Understanding includes connecting number calculations with counting sequences, partitioning and combining numbers flexibly,

identifying and describing the relationship between addition and subtraction and between multiplication and division

Fluency includes counting numbers in sequences readily, using informal units iteratively to compare measurements, using the

language of chance to describe outcomes of familiar chance events and describing and comparing time durations

Problem Solving includes formulating problems from authentic situations, making models and using number sentences that

represent problem situations, and matching transformations with their original shape

Reasoning includes using known facts to derive strategies for unfamiliar calculations, comparing and contrasting related models

of operations, and creating and interpreting simple representations of data



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4/18

Recognise and represent multiplication as repeated

addition, groups and arrays (ACMNA031)

Recognise and represent division as grouping into

equal sets and solve simple problems using these

representations (ACMNA032)


Recognise and interpret common uses of halves,

quarters and eighths of shapes and collections

(ACMNA033)


Count and order small collections of Australian coins

and notes according to their value (ACMNA034)


Describe patterns with numbers and identify missing

elements (ACMNA035)

Solve problems by using number sentences for

addition or subtraction (ACMNA036)

Describe the features of three-dimensional objects

(ACMMG043)


Interpret simple maps of familiar locations and identify

the relative positions of key features (ACMMG044)

Investigate the effect of one-step slides and flips withand without digital technologies (ACMMG045)

Identify and describe half and quarter turns

(ACMMG046)


By the end of Year 2, students recognise increasing and decreasing number sequences involving 2s, 3s and 5s. They represent

multiplication and division by grouping into sets. They associate collections of Australian coins with their value. Students identify

the missing element in a number sequence. Students recognise the features of three-dimensional objects. They interpret simple

maps of familiar locations. They explain the effects of one-step transformations. Students make sense of collected information.

Students count to and from 1000. They perform simple addition and subtraction calculations using a range of strategies. They

divide collections and shapes into halves, quarters and eighths. Students order shapes and objects using informal units. They

tell time to the quarter hour and use a calendar to identify the date and the months included in seasons. They draw two-

dimensional shapes. They describe outcomes for everyday events. Students collect data from relevant questions to create lists,

tables and picture graphs.

Year 2 Work Samples


Year 3Year 3 Level Description





At this year level:

Understanding includes connecting number representations with number sequences, partitioning and combining numbers

flexibly, representing unit fractions, using appropriate language to communicate times, and identifying environmental symmetry

Fluency includes recalling multiplication facts, using familiar metric units to order and compare objects, identifying and describing

outcomes of chance experiments, interpreting maps and communicating positions

Problem Solving includes formulating and modelling authentic situations involving planning methods of data collection and

representation, making models of three-dimensional objects and using number properties to continue number patterns


18 13/9/2012 3:00 PM


5/18

Number and Algebra


Investigate the conditions required for a number to be

odd or even and identify odd and even numbers

(ACMNA051)

Recognise, model, represent and order numbers to at

least 10 000 (ACMNA052)

Apply place value to partition, rearrange and regroup

numbers to at least 10 000 to assist calculations and

solve problems (ACMNA053)

Recognise and explain the connection between

addition and subtraction (ACMNA054)

Recall addition facts for single-digit numbers and

related subtraction facts to develop increasingly

efficient mental strategies for computation

(ACMNA055)

Recall multiplication facts of two, three, five and ten

and related division facts (ACMNA056)

Represent and solve problems involving multiplication

using efficient mental and written strategies and

appropriate digital technologies (ACMNA057)


Model and represent unit fractions including 1/2, 1/4,

1/3, 1/5 and their multiples to a complete whole

(ACMNA058)


Represent money values in multiple ways and count

the change required for simple transactions to the

nearest five cents (ACMNA059)


Describe, continue, and create number patterns

resulting from performing addition or subtraction

(ACMNA060)



Measure, order and compare objects using familiar

metric units of length, mass and capacity

(ACMMG061)

Tell time to the minute and investigate the relationship

between units of time (ACMMG062)

Shape

Make models of three-dimensional objects and

describe key features (ACMMG063)


Create and interpret simple grid maps to show

position and pathways (ACMMG065)

Identify symmetry in the environment (ACMMG066)

Geometric reasoning

Identify angles as measures of turn and compare

angle sizes in everyday situations (ACMMG064)

Statistic

Chance

Conduc

possible

(ACMSP

Data re

Identify

Identify

collectio

Collect

displays

column

technol

Interpret

Reasoning includes using generalising from number properties and results of calculations, comparing angles, creating and

interpreting variations in the results of data collections and data displays



By the end of Year 3, students recognise the connection between addition and subtraction and solve problems using efficient

strategies for multiplication. They model and represent unit fractions. They represent money values in various ways. Students

identify symmetry in the environment. They match positions on maps with given information. Students recognise angles in real

situations. They interpret and compare data displays.

Students count to and from 10 000. They classify numbers as either odd or even. They recall addition and multiplication facts for

single digit numbers. Students correctly count out change from financial transactions. They continue number patterns involving

addition and subtraction. Students use metric units for length, mass and capacity. They tell time to the nearest minute. Students

make models of three-dimensional objects. Students conduct chance experiments and list possible outcomes. They carry out


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6/18

Number and Algebra


Investigate and use the properties of odd and even

numbers (ACMNA071)

Recognise, represent and order numbers to at least

tens of thousands (ACMNA072)

Apply place value to partition, rearrange and regroup

numbers to at least tens of thousands to assist

calculations and solve problems (ACMNA073)

Investigate number sequences involving multiples of

3, 4, 6, 7, 8, and 9 (ACMNA074)

Recall multiplication facts up to 10 10 and related

division facts (ACMNA075)

Develop efficient mental and written strategies and

use appropriate digital technologies for multiplication

and for division where there is no remainder

(ACMNA076)


Investigate equivalent fractions used in contexts

(ACMNA077)



Use scaled instruments to measure and compare

lengths, masses, capacities and temperatures

(ACMMG084)

Compare objects using familiar metric units of area

and volume (ACMMG290)

Convert between units of time (ACMMG085)

Use am and pm notation and solve simple time

problems (ACMMG086)

Shape

Compare the areas of regular and irregular shapes by

informal means (ACMMG087)

Compare and describe two dimensional shapes that

result from combining and splitting common shapes,

with and without the use of digital technologies

(ACMMG088)


Use simple scales, legends and directions to interpret

Statistic

Chance

Describ

chances

Identify

the othe

Identify

affected

Data re

Select a

survey

Constru

use of di

data. In

graphs

values (

Evaluatillustrati

(ACMSP

simple data investigations for categorical variables.

Year 3 Work Samples


Year 4Year 4 Level Description





At this year level:

Understanding includes making connections between representations of numbers, partitioning and combining numbers flexibly,

extending place value to decimals, using appropriate language to communicate times, and describing properties of symmetrical

shapes

Fluency includes recalling multiplication tables, communicating sequences of simple fractions, using instruments to measure

accurately, creating patterns with shapes and their transformations, and collecting and recording data

Problem Solving includes formulating, modelling and recording authentic situations involving operations, comparing large

numbers with each other, comparing time durations, and using properties of numbers to continue patterns

Reasoning includes using generalising from number properties and results of calculations, deriving strategies for unfamiliar

multiplication and division tasks, comparing angles, communicating information using graphical displays and evaluating the

appropriateness of different displays



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7/18

Count by quarters halves and thirds, including with

mixed numerals. Locate and represent these fractions

on a number line (ACMNA078)

Recognise that the place value system can be

extended to tenths and hundredths. Make

connections between fractions and decimal notation

(ACMNA079)


Solve problems involving purchases and the

calculation of change to the nearest five cents with

and without digital technologies (ACMNA080)


Explore and describe number patterns resulting from

performing multiplication (ACMNA081)

Solve word problems by using number sentencesinvolving multiplication or division where there is no

remainder (ACMNA082)

Use equivalent number sentences involving addition

and subtraction to find unknown quantities

(ACMNA083)

information contained in basic maps (ACMMG090)

Create symmetrical patterns, pictures and shapes with

and without digital technologies (ACMMG091)

Geometric reasoning

Compare angles and classify them as equal to,

greater than or less than a right angle (ACMMG089)


By the end of Year 4, students choose appropriate strategies for calculations involving multiplication and division. They

recognise common equivalent fractions in familiar contexts and make connections between fraction and decimal notations up to

two decimal places. Students solve simple purchasing problems. They identify unknown quantities in number sentences. They

describe number patterns resulting from multiplication. Students compare areas of regular and irregular shapes using informalunits. They solve problems involving time duration. They interpret information contained in maps. Students identify dependent

and independent events. They describe different methods for data collection and representation, and evaluate their

effectiveness.

Students use the properties of odd and even numbers. They recall multiplication facts to 10 x 10 and related division facts.

Students locate familiar fractions on a number line. They continue number sequences involving multiples of single digit numbers.

Students use scaled instruments to measure temperatures, lengths, shapes and objects. They convert between units of time.

Students create symmetrical shapes and patterns. They classify angles in relation to a right angle. Students list the probabilities

of everyday events. They construct data displays from given or collected data.

Year 4 Work Samples


Year 5






At this year level:

Understanding includes making connections between representations of numbers, using fractions to represent probabilities,

comparing and ordering fractions and decimals and representing them in various ways, describing transformations and


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8/18

Number and Algebra


Identify and describe factors and multiples of whole

numbers and use them to solve problems

(ACMNA098)

Use estimation and rounding to check the

reasonableness of answers to calculations

(ACMNA099)

Solve problems involving multiplication of large

numbers by one- or two-digit numbers using efficient

mental, written strategies and appropriate digital

technologies (ACMNA100)

Solve problems involving division by a one digit

number, including those that result in a remainder

(ACMNA101)

Use efficient mental and written strategies and apply

appropriate digital technologies to solve problems

(ACMNA291)


Compare and order common unit fractions and locate

and represent them on a number line (ACMNA102)

Investigate strategies to solve problems involving

addition and subtraction of fractions with the same

denominator (ACMNA103)

Recognise that the place value system can be

extended beyond hundredths (ACMNA104)

Compare, order and represent decimals (ACMNA105)


Create simple financial plans (ACMNA106)


Describe, continue and create patterns with fractions,

decimals and whole numbers resulting from addition

and subtraction (ACMNA107)



Choose appropriate units of measurement for length,

area, volume, capacity and mass (ACMMG108)

Calculate the perimeter and area of rectangles using

familiar metric units (ACMMG109)

Compare 12- and 24-hour time systems and convert

between them (ACMMG110)

Shape

Connect three-dimensional objects with their nets and

other two-dimensional representations (ACMMG111)


Use a grid reference system to describe locations.Describe routes using landmarks and directional

language (ACMMG113)

Describe translations, reflections and rotations of

two-dimensional shapes. Identify line and rotational

symmetries (ACMMG114)

Apply the enlargement transformation to familiar two

dimensional shapes and explore the properties of the

resulting image compared with the original

(ACMMG115)

Geometric reasoning

Estimate, measure and compare angles using

degrees. Construct angles using a protractor

(ACMMG112)

Statistic

Chance

List outc

likely ou

outcom

Recogni

(ACMSP

Data re

Pose qu

data by

Constru

and tabl

the use

Describ

(ACMSP

identifying line and rotational symmetry

Fluency includes choosing appropriate units of measurement for calculation of perimeter and area, using estimation to check the

reasonableness of answers to calculations and using instruments to measure angles

Problem Solving includes formulating and solving authentic problems using whole numbers and measurements and creating

financial plans

Reasoning includes investigating strategies to perform calculations efficiently, continuing patterns involving fractions and

decimals, interpreting results of chance experiments, posing appropriate questions for data investigations and interpreting data

sets



18 13/9/2012 3:00 PM


9/18

Use equivalent number sentences involving

multiplication and division to find unknown quantities

(ACMNA121)

Number and Algebra


Identify and describe properties of prime, composite,

square and triangular numbers (ACMNA122)

Select and apply efficient mental and written

strategies and appropriate digital technologies to

solve problems involving all four operations with

whole numbers (ACMNA123)



Connect decimal representations to the metric system

(ACMMG135)

Convert between common metric units of length, mass

and capacity (ACMMG136)

Statistic

Chance

Describ

percent

Conduc

large nu

technol

Compar


By the end of Year 5, students solve simple problems involving the four operations using a range of strategies. They check the

reasonableness of answers using estimation and rounding. Students identify and describe factors and multiples. They explain

plans for simple budgets. Students connect three-dimensional objects with their two-dimensional representations. They describe

transformations of two-dimensional shapes and identify line and rotational symmetry. Students compare and interpret different

data sets.

Students order decimals and unit fractions and locate them on number lines. They add and subtract fractions with the same

denominator. Students continue patterns by adding and subtracting fractions and decimals. They find unknown quantities in

number sentences. They use appropriate units of measurement for length, area, volume, capacity and mass, and calculate

perimeter and area of rectangles. They convert between 12 and 24 hour time. Students use a grid reference system to locate

landmarks. They measure and construct different angles. Students list outcomes of chance experiments with equally likely

outcomes and assign probabilities between 0 and 1. Students pose questions to gather data, and construct data displays

appropriate for the data.

Year 5 Work Samples


Year 6






At this year level:

Understanding includes describing properties of different sets of numbers, using fractions and decimals to describe probabilities,

representing fractions and decimals in various ways and describing connections between them, and making reasonable

estimations

Fluency includes representing integers on a number line, calculating simple percentages, using brackets appropriately,

converting between fractions and decimals, using operations with fractions, decimals and percentages, measuring using metric

units, and interpreting timetables

Problem Solving includes formulating and solving authentic problems using fractions, decimals, percentages and

measurements, interpreting secondary data displays, and finding the size of unknown angles

Reasoning includes explaining mental strategies for performing calculations, describing results for continuing numbersequences, explaining the transformation of one shape into another, explaining why the actual results of chanceexperiments may

differ from expected results



18 13/9/2012 3:00 PM


10/18

Investigate everyday situations that use integers.

Locate and represent these numbers on a number line

(ACMNA124)


Compare fractions with related denominators and

locate and represent them on a number line

(ACMNA125)

Solve problems involving addition and subtraction of

fractions with the same or related denominators

(ACMNA126)

Find a simple fraction of a quantity where the result is

a whole number, with and without digital technologies

(ACMNA127)

Add and subtract decimals, with and without digital

technologies, and use estimation and rounding to

check the reasonableness of answers (ACMNA128)

Multiply decimals by whole numbers and perform

divisions by non-zero whole numbers where the

results are terminating decimals, with and without

digital technologies (ACMNA129)

Multiply and divide decimals by powers of 10

(ACMNA130)

Make connections between equivalent fractions,

decimals and percentages (ACMNA131)


Investigate and calculate percentage discounts of

10%, 25% and 50% on sale items, with and without



Continue and create sequences involving whole

numbers, fractions and decimals. Describe the rule

used to create the sequence (ACMNA133)

Explore the use of brackets and order of operations to

write number sentences (ACMNA134)

Solve problems involving the comparison of lengths

and areas using appropriate units (ACMMG137)

Connect volume and capacity and their units of

measurement (ACMMG138)

Interpret and use timetables (ACMMG139)

Shape

Construct simple prisms and pyramids (ACMMG140)


Investigate combinations of translations, reflections

and rotations, with and without the use of digital

technologies (ACMMG142)

Introduce the Cartesian coordinate system using all

four quadrants (ACMMG143)

Geometric reasoning

Investigate, with and without digital technologies,

angles on a straight line, angles at a point and

vertically opposite angles. Use results to find

unknown angles (ACMMG141)

with exp

Data re

Interpret

includin

categori

Interpret

and els


By the end of Year 6, students recognise the properties of prime, composite, square and triangular numbers. They describe the

use of integers in everyday contexts. They solve problems involving all four operations with whole numbers. Students connect

fractions, decimals and percentages as different representations of the same number. They solve problems involving the addition

and subtraction of related fractions. Students make connections between the powers of 10 and the multiplication and division of

decimals. They describe rules used in sequences involving whole numbers, fractions and decimals. Students connect decimal

representations to the metric system and choose appropriate units of measurement to perform a calculation. They make

connections between capacity and volume. They solve problems involving length and area. They interpret timetables. Students

describe combinations of transformations. They solve problems using the properties of angles. Students compare observed andexpected frequencies. They interpret and compare a variety of data displays including those displays for two categorical

variables. They evaluate secondary data displayed in the media.

Students locate fractions and integers on a number line. They calculate a simple fraction of a quantity. They add, subtract and

multiply decimals and divide decimals where the result is rational. Students calculate common percentage discounts on sale


f 18 13/9/2012 3:00 PM


11/18

Number and Algebra


Investigate index notation and represent whole

numbers as products of powers of prime numbers

(ACMNA149)

Investigate and use square roots of perfect square

numbers (ACMNA150)

Apply the associative, commutative and distributive

laws to aid mental and written computation(ACMNA151)

Compare, order, add and subtract integers

(ACMNA280)

Real numbers

Compare fractions using equivalence. Locate and

represent positive and negative fractions and mixed

numbers on a number line (ACMNA152)

Solve problems involving addition and subtraction offractions, including those with unrelated denominators

(ACMNA153)

Multiply and divide fractions and decimals using



Establish the formulas for areas of rectangles,

triangles and parallelograms and use these in problem

solving (ACMMG159)

Calculate volumes of rectangular prisms

(ACMMG160)

Shape

Draw different views of prisms and solids formed from

combinations of prisms (ACMMG161)


Describe translations, reflections in an axis, and

rotations of multiples of 90 on the Cartesian plane

using coordinates. Identify line and rotational

symmetries (ACMMG181)

Geometric reasoning

Identify corresponding, alternate and co-interiorangles when two straight lines are crossed by a

transversal (ACMMG163)

Investigate conditions for two lines to be parallel and

Statistic

Chance

Constru

withequ

Assign

determi

Data re

Identifydata coll

(ACMSP

Constru

includin

(ACMSP

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data. Int

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Describmean a

items. They write correct number sentences using brackets and order of operations. Students locate an ordered pair in any one

of the four quadrants on the Cartesian plane. They construct simple prisms and pyramids. Students list and communicate

probabilities using simple fractions, decimals and percentages.

Year 6 Work Samples


Year 7






At this year level:

Understanding includes describing patterns in uses of indices with whole numbers, recognising equivalences between fractions,

decimals, percentages and ratios, plotting points on the Cartesian plane, identifying angles formed by a transversal crossing apair of lines, and connecting the laws and properties of numbers to algebraic terms and expressions

Fluency includes calculating accurately with integers, representing fractions and decimals in various ways, investigating best

buys, finding measures of central tendency and calculating areas of shapes and volumes of prisms

Problem Solving includes formulating and solving authentic problems using numbers and measurements,working with

transformations and identifying symmetry, calculating angles and interpreting sets of data collected through chance experiments

Reasoning includes applying the number laws to calculations, applying known geometric facts to draw conclusions about

shapes, applying an understanding of ratio and interpreting data displays



f 18 13/9/2012 3:00 PM


12/18

efficientwritten strategies and digital technologies

(ACMNA154)

Express one quantity as a fraction of another, with

and without the use of digital technologies

(ACMNA155)

Round decimals to a specified number of decimal

places (ACMNA156)

Connect fractions, decimals and percentages and

carry out simple conversions (ACMNA157)

Find percentages of quantities and express one

quantity as a percentage of another, with and without

digital technologies. (ACMNA158)

Recognise and solve problems involving simple ratios

(ACMNA173)


Investigate and calculate 'best buys', with and without



Introduce the concept of variables as a way of

representing numbers using letters (ACMNA175)

Create algebraic expressions and evaluate them by

substituting a given value for each variable

(ACMNA176)

Extend and apply the laws and properties of arithmetic

to algebraic terms and expressions (ACMNA177)

Linear and non-linear relationships

Given coordinates, plot points on the Cartesian plane,

and find coordinates for a given point (ACMNA178)

Solve simple linear equations (ACMNA179)

Investigate, interpret and analyse graphs fromauthentic data (ACMNA180)

solve simple numerical problems using reasoning

(ACMMG164)

Demonstrate that the angle sum of a triangle is 180

and use this to find the angle sum of a quadrilateral

(ACMMG166)

Classify triangles according to their side and angle

properties and describe quadrilaterals (ACMMG165)


By the end of Year 7, students solve problems involving the comparison, addition and subtraction of integers. They make the

connections between whole numbers and index notation and the relationship between perfect squares and square roots. They

solve problems involving percentages and all four operations with fractions and decimals. They compare the cost of items to

make financial decisions. Students represent numbers using variables. They connect the laws and properties for numbers to

algebra. They interpret simple linear representations and model authentic information. Students describe different views of three-

dimensional objects. They represent transformations in the Cartesian plane. They solve simple numerical problems involving

angles formed by a transversal crossing two parallel lines. Students identify issues involving the collection of continuous data.

They describe the relationship between the median and mean in data displays.

Students use fractions, decimals and percentages, and their equivalences. They express one quantity as a fraction or

percentage of another. Students solve simple linear equations and evaluate algebraic expressions after numerical substitution.

They assign ordered pairs to given points on the Cartesian plane. Students use formulas for the area and perimeter of

rectangles and calculate volumes of rectangular prisms. Students classify triangles and quadrilaterals. They name the types of

angles formed by a transversal crossing parallel line. Students determine the sample space for simple experiments with equally


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Number and Algebra


Use index notation with numbers to establish the

index laws with positive integral indices and the zero

index (ACMNA182)

Carry out the four operations with rational numbers

and integers, using efficient mental and written

strategies and appropriate digital technologies

(ACMNA183)

Real numbers

Investigate terminating and recurring decimals

(ACMNA184)

Investigate the concept of irrational numbers,

including (ACMNA186)

Solve problems involving the use of percentages,

including percentage increases and decreases, with

and without digital technologies (ACMNA187)

Solve a range of problems involving rates and ratios,

with and without digital technologies (ACMNA188)




Choose appropriate units of measurement for area

and volume and convert from one unit to another

(ACMMG195)

Find perimeters and areas of parallelograms,

trapeziums, rhombuses and kites (ACMMG196)

Investigate the relationship between features of

circles such as circumference, area, radius anddiameter. Use formulas to solve problems involving

circumference and area (ACMMG197)

Develop the formulas for volumes of rectangular and

triangular prisms and prisms in general. Use formulas

to solve problems involving volume (ACMMG198)

Solve problems involving duration, including using 12-

and 24-hour time within a single time zone

(ACMMG199)

Geometric reasoning

Define congruence of plane shapes using

transformations (ACMMG200)

Statistic

Chance

Identify

probabili

Describ

'or' (A or

and 'an

Repres

diagram

Data re

Investig

census,

Explore

data thr

process

Explore

random(ACMSP

Investig

includin

likely outcomes and assign probabilities to those outcomes. They calculate mean, mode, median and range for data sets . They

construct stem-and-leaf plots and dot-plots.

Year 7 Work Samples


Year 8






At this year level:

Understanding includes describing patterns involving indices and recurring decimals, identifying commonalities between

operations with algebra and arithmetic, connecting rules for linear relations their graphs, explaining the purpose of statistical

measures, and explaining measurements of perimeter and area

Fluency includes calculating accurately with simple decimals, indices and integers, recognising equivalence of common decimals

and fractions including recurring decimals, factorising and simplifying basic algebraic expressions, and evaluating perimeters,

areas of common shapes and their volumes and three dimensional objects

Problem Solving includes formulating, and modelling practical situations involving ratios, profit and loss, areas and perimeters

of common shapes, and using two-way tables and Venn diagrams to calculate probabilities

Reasoning includes justifying the result of a calculation or estimation as reasonable, deriving probability from its complement,

using congruence to deduce properties of triangles, finding estimates of means and proportions of populations



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Solve problems involving profit and loss, with and

withoutdigital technologies (ACMNA189)


Extend and apply the distributive law to the expansion

of algebraic expressions (ACMNA190)

Factorise algebraic expressions by identifyingnumerical factors (ACMNA191)

Simplify algebraic expressions involving the four

operations (ACMNA192)


Plot linear relationships on the Cartesian plane with

and without the use of digital technologies

(ACMNA193)

Solve linear equations using algebraic and graphicaltechniques. Verify solutions by substitution

(ACMNA194)

Develop the conditions for congruence of triangles

(ACMMG201)

Establish properties of quadrilaterals using congruent

triangles and angle properties, and solve related

numerical problems using reasoning (ACMMG202)

(ACMSP


By the end of Year 8, students solve everyday problems involving rates, ratios and percentages. They recognise index laws and

apply them to whole numbers. They describe rational and irrational numbers. Students solve problems involving profit and loss.

They make connections between expanding and factorising algebraic expressions. Students solve problems relating to the

volume of prisms. They make sense of time duration in real applications. They identify conditions for the congruence of triangles

and deduce the properties of quadrilaterals. Students model authentic situations with two-way tables and Venn diagrams. They

choose appropriate language to describe events and experiments. They explain issues related to the collection of data and the

effect of outliers on means and medians in that data.

Students use efficient mental and written strategies to carry out the four operations with integers. They simplify a variety of

algebraic expressions. They solve linear equations and graph linear relationships on the Cartesian plane. Students convert

between units of measurement for area and volume. They perform calculations to determine perimeter and area of

parallelograms, rhombuses and kites. They name the features of circles and calculate the areas and circumferences of circles.

Students determine complementary events and calculate the sum of probabilities.

Year 8 Work Samples


Year 9






At this year level:

Understanding includes describing the relationship between graphs and equations, simplifying a range of algebraic expressions,

explaining the use of relative frequencies to estimate probabilities, and the use of the trigonometric ratios for right-angle triangles

Fluency includes applying the index laws to expressions with integer indices, expressing numbers in scientific notation, listing

outcomes for experiments and developing familiarity with calculations involving the Cartesian plane and calculating areas of

shapes and surface areas of prisms

Problem Solving includes formulating, and modelling practical situations involving surface areas and volumes of right prisms,


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Number and Algebra

Real numbers

Solve problems involving direct proportion. Explore

the relationship between graphs and equations

corresponding to simple rate problems (ACMNA208)

Apply index laws to numerical expressions with integer

indices (ACMNA209)

Express numbers in scientific notation (ACMNA210)


Solve problems involving simple interest (ACMNA211)


Extend and apply the index laws to variables, using

positive integer indices and the zero index

(ACMNA212)

Apply the distributive law to the expansion of algebraic

expressions, including binomials, and collect like

terms where appropriate (ACMNA213)


Find the distance between two points located on a

Cartesian plane using a range of strategies, including

graphing software (ACMNA214)

Find the midpoint and gradient of a line segment

(interval) on the Cartesian plane using a range of

strategies, including graphing software (ACMNA294)

Sketch linear graphs using the coordinates of twopoints and solve linear equations (ACMNA215)

Graph simple non-linear relations with and without the

use of digital technologies and solve simple related

equations (ACMNA296)



Calculate the areas of composite shapes

(ACMMG216)

Calculate the surface area and volume of cylinders

and solve related problems (ACMMG217)

Solve problems involving the surface area and volume

of right prisms (ACMMG218)

Investigate very small and very large time scales and

intervals (ACMMG219)

Geometric reasoning

Use the enlargement transformation to explain

similarity and develop the conditions for triangles to

be similar (ACMMG220)

Solve problems using ratio and scale factors in similar

figures (ACMMG221)

Pythagoras and trigonometry

Investigate Pythagoras Theorem and its application

to solving simple problems involving right angled

triangles (ACMMG222)

Use similarity to investigate the constancy of the sine,

cosine and tangent ratios for a given angle in right-

angled triangles (ACMMG223)

Apply trigonometry to solve right-angled triangle

problems (ACMMG224)

Statistic

Chance

List all o

both wit

diagram

and det

Calculat

data to

or 'or' (A

Investigelsewhe

to estim

(ACMSP

Data re

Identify

least on

variable,

sources

Construhistogra

skewed

Compar

range to

terms of

applying ratio and scale factors to similar figures, solving problems involving right-angle trigonometry, and collecting data from

secondary sources to investigate an issue

Reasoning includes following mathematical arguments, evaluating media reports and using statistical knowledge to clarify

situations, developing strategies in investigating similarity and sketching linear graphs



By the end of Year 9, students solve problems involving simple interest. They interpret ratio and scale factors in similar figures.

Students explain similarity of triangles. They recognise the connections between similarity and the trigonometric ratios. Students

compare techniques for collecting data in primary and secondary sources. They make sense of the position of the mean and

median in skewed, symmetric and bi-modal displays to describe and interpret data.

Students apply the index laws to numbers and express numbers in scientific notation. They expand binomial expressions. They

find the distance between two points on the Cartesian plane and the gradient and midpoint of a line segment. They sketch linear

and non-linear relations. Students calculate areas of shapes and the volume and surface area of right prisms and cylinders.

They use Pythagoras Theorem and trigonometry to find unknown sides of right-angled triangles. Students calculate relative


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Number and Algebra


Connect the compound interest formula to repeated

applications of simple interest using appropriate digital

technologies (ACMNA229)


Factorise algebraic expressions by taking out a

common algebraic factor (ACMNA230)

Simplify algebraic products and quotients using index

laws (ACMNA231)

Apply the four operations to simple algebraic fractions

with numerical denominators (ACMNA232)

Expand binomial products and factorise monic

quadratic expressions using a variety of strategies

(ACMNA233)

Substitute values into formulas to determine an

unknown (ACMNA234)


Solve problems involving linear equations, including



Solve problems involving surface area and volume for

a range of prisms, cylinders and composite solids

(ACMMG242)

Geometric reasoning

Formulate proofs involving congruent triangles and

angle properties (ACMMG243)

Apply logical reasoning, including the use of

congruence and similarity, to proofs and numerical

exercises involving plane shapes (ACMMG244)


Solve right-angled triangle problems including those

involving direction and angles of elevation and

depression (ACMMG245)

Statistic

Chance

Describ

experim

assign p

probabili

indepen

Use the

that to i

common(ACMSP

Data re

Determi

(ACMSP

Constru

compar

Compar

histogra

Use sca

relation

(ACMSP

frequencies to estimate probabilities, list outcomes for two-step experiments and assign probabilities for those outcomes. They

construct histograms and back-to-back stem-and-leaf plots.

Year 9 Work Samples


Year 10






At this year level:

Understanding includes applying the four operations to algebraic fractions, finding unknowns in formulas after substitution,

making the connection between equations of relations and their graphs, comparing simple and compound interest in financial

contexts and determining probabilities of two and three step experiments

Fluency includes factorising and expanding algebraic expressions, using a range of strategies to solve equations and using

calculations to investigate ing the shape of data sets

Problem Solving includes calculating the surface area and volume of a diverse range of prisms to solve practical problems,

finding unknown lengths and angles using applications of trigonometry, using algebraic and graphical techniques to find

solutions to simultaneous equations and inequalities, and investigating independence of events

Reasoning includes formulating geometric proofs involving congruence and similarity, interpreting and evaluating media

statements and interpreting and comparing data sets



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those derived from formulas (ACMNA235)

Solve linear inequalities and graph their solutions on a

number line (ACMNA236)

Solve linear simultaneous equations, using algebraic

and graphical techniques including using digital

technology (ACMNA237)

Solve problems involving parallel and perpendicular

lines (ACMNA238)

Explore the connection between algebraic and

graphical representations of relations such as simple

quadratics, circles and exponentials using digital

technology as appropriate (ACMNA239)

Solve linear equations involving simple algebraic

fractions (ACMNA240)

Solve simple quadratic equations using a range ofstrategies (ACMNA241)

Investigate and describe bivariate numerical data

where the independent variable is time (ACMSP252)

Evaluate statistical reports in the media and other

places by linking claims to displays, statistics and

representative data (ACMSP253)

Number and Algebra

Real numbers

Define rational and irrational numbers and perform

operations with surds and fractional indices

(ACMNA264)

Use the definition of a logarithm to establish and apply

the laws of logarithms (ACMNA265)


Investigate the concept of a polynomial and apply the



Solve problems involving surface area and volume of

right pyramids, right cones, spheres and related

composite solids (ACMMG271)

Geometric reasoning

Prove and apply angle and chord properties of circles

(ACMMG272)


Statistic

Chance

Investig

elsewhe

impleme

Data re

Calculat

deviatio

(ACMSP


By the end of Year 10, students recognise the connection between simple and compound interest. They solve problems involving

linear equations and inequalities. They make the connections between algebraic and graphical representations of relations.

Students solve surface area and volume problems relating to composite solids. They recognise the relationships between

parallel and perpendicular lines. Students apply deductive reasoning to proofs and numerical exercises involving plane shapes.

They compare data sets by referring to the shapes of the various data displays. They describe bivariate data where the

independent variable is time. Students describe statistical relationships between two continuous variables. They evaluate

statistical reports.

Students expand binomial expressions and factorise monic quadratic expressions. They find unknown values after substitutioninto formulas. They perform the four operations with simple algebraic fractions. Students solve simple quadratic equations and

pairs of simultaneous equations. They use triangle and angle properties to prove congruence and similarity. Students use

trigonometry to calculate unknown angles in right-angled triangles. Students list outcomes for multi-step chance experiments and

assign probabilities for these experiments. They calculate quartiles and inter-quartile ranges.

Year 10 Work Samples


Year 10A

Year 10A Content Descriptions


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factor and remainder theorems to solve problems

(ACMNA266)


Solve simple exponential equations (ACMNA270)

Describe, interpret and sketch parabolas, hyperbolas,

circles and exponential functions and their

transformations (ACMNA267)

Apply understanding of polynomials to sketch a range

of curves and describe the features of these curves

from their equation (ACMNA268)

Factorise monic and non-monic quadratic expressions

and solve a wide range of quadratic equations derived

from a variety of contexts (ACMNA269)

Establish the sine, cosine and area rules for any

triangle and solve related problems (ACMMG273)

Use the unit circle to define trigonometric functions,

and graph them with and without the use of digital

technologies (ACMMG274)

Solve simple trigonometric equations (ACMMG275)

Apply Pythagoras theorem and trigonometry to

solving three-dimensional problems in right-angled

triangles (ACMMG276)

Use info

numeric

line to d

(ACMSP


the australian curriculum v3

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